Goodness-of-Fit Tests and Model Validity

The 37 expository articles in this volume provide broad coverage of important topics relating to the theory, methods, and applications of goodness-of-fit tests and model validity. The book is divided into eight parts, each of which presents topics written by expert researchers in their areas.

Key features include:

• state-of-the-art exposition of modern model validity methods, graphical techniques, and computer-intensive methods

• systematic presentation with sufficient history and coverage of the fundamentals of the subject

• exposure to recent research and a variety of open problems

• many interesting real-life examples for practitioners

• extensive bibliography, with special emphasis on recent literature

• subject index

This comprehensive reference work will serve the statistical and applied mathematics communities as well as practitioners in the field.

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Preface Contributors List of Tables List of Figures ---------------------- Part I. History and Fundamentals Karl Pearson and the Chi-Squared Test / D.R. Cox Karl Pearson Chi-Square Test-The Dawn of Statistical Inference / C.R. Rao Approximate Models / P.J. Huber -------------------- Part II. Chi-Squared Test Partitioning the Pearson-Fisher Chi-Squared Goodness-of-Fit Statistic / G.D. Rayner Statistical Tests for Normal Family in Presence of Outlying Observations / A. Zerbet Chi-Squared Test for the Law of Annual Death Rates: Case with Censure for Life Insurance Files / L. Gerville-Reache ------------------------ Part III. Goodness-of-Fit Tests for Parametric Distributions Shapiro-Wilk Type Goodness-of-Fit Tests for Normality: Asymptotics Revisited / P. Kumar A Test for Exponentiality Based on Spacings for Progressively Type II Censored Data / N. Balakrishnan, H.K.T. Ng, and N. Kannan Goodness-of- Fit Statistics for the Exponential Distribution When the Data are Grouped / S. Gulati and J. Neus Characterization Theorems and Goodness-of-Fit Tests / C.E. Marchetti and G.S. Mudholkar Goodness-of-Fit Tests Based on Record Data and Generalized Ranked Set Data / B.C. Arnold, R.J. Beaver, E. Castillo, and J.M. Sarabia ------------------------------- Part IV. Regression and Goodness-of-Fit Tests Gibbs Regression and a Test of Goodness-of-Fit / L. Seymour A CLT for the L_2 Norm of the Regression Estimators Under alpha-Mixing: Application to G-O-F Tests / C.A.T. Diack Testing theGoodness-of-Fit of a Linear Model in Nonparametric Regression / Z. Mohdeb and A. Mokkadem A New Test of Linear Hypothesis in Regression / Y. Baraud, S. Huet, and B. Laurent ------------------------------------- Part V. Goodness-of-Fit Tests in Survival Analysis and Reliability Inference in Extensions of the Cox Model for Heterogeneous Populations / O. Pons Assumptions of a Latent Survival Model / M.-L. Ting Lee and G.A. Whitmore Goodness-of-Fit Testing of the Cox Proportional Hazards Model / K. Devarajan and N. Ebrahimi A New Family of Multivariate Distributions for Survival Data / S.T. Gross and C. Huber-Carol Discrimination Index, the Area Under to ROC Curve / B.-H. Nam and R. B. D'Agostino Goodness-of-Fit Tests for Accelerated Life Models / V. Bagdonavicius and M.S. Nikulin ------------------------------ Part VI. Graphic Methods and General Goodness-of-Fit Tests Two Nonstandard Examples of the Classical Stratification Approach to Graphically Assessing Proportionality of Hazards / N. Keiding Association in Contingency Tables, Correspondence Analysis, and (Modified) Andrews Plots / R. Khattree and D.N. Naik Orthogonal Expansions and Distinction Between Logistic and Normal / C.M. Cuadras and D. Cuadras Functional Tests of Fit / D. Bosq Quasi Most Powerful Invariant Tests of Goodness-of-Fit --------------------------------- Part VII. Model Validity in Quality of Life Test of Monotonicity for the Rasch Model J. Bretagnolle Validation of Model Assumptions in Quality of Life Measurements / A. Hamon, J.F. Dupuy, and M. Mesbah &nbsp